Gravitational waves in singular and bouncing FLRW universes

We investigate propagation of gravitational waves in two models belonging to the Friedman-Lemaître-Robertson-Walker (FLRW) class of cosmologies: the singular Einstein-Maxwell Universe (EMU), which has an electromagnetic field described by Maxwell’s electrodynamics as the source of its geometry, and the bouncing Nonlinear Electrodynamics Universe (NLEU), which has the electromagnetic field described by a nonlinear generalization of Maxwell’s electrodynamics as the source of its geometry. We work with an explicitly gauge-independent formulation of cosmological perturbations in FLRW models and analyze the qualitative features of the dynamical system that describes the propagation of primordial tensorial perturbations in both geometries. Based on this analysis, we show that gravitational waves generated near a singularity or a bounce exhibit qualitatively different behavior.